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$q$-Generalized representation of the $d$-dimensional Dirac delta and $q$-Fourier transform (1705.01584v2)
Published 3 May 2017 in math-ph, cond-mat.stat-mech, and math.MP
Abstract: We discuss a generalized representation of the Dirac delta function in $d$ dimensions in terms of $q$-exponential functions. We apply this new representation to the study of the so-called $q$-Fourier transform, proving its invertibility for any value of $d$. We finally illustrate the effect of the $q$-deformation on the Gibbs phenomenon.
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